If the terminal is EMV certified, it should prioritise EMV contactless. If not, I belive it will fall back to chip or swipe (like you said).
If these are not available… Well, I think that would be a straight decline… (at that point the merchant should really consider upgrading their terminal!)
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Maybe I’m wrong. If you read the thousands of pages of the EMV Specification and the payment specifications before EMV existed, feel free to correct me 
Yeah, even though the liability shift was in 2015. Many terminals are still not upgraded. If they have been the chip functionality is usually disabled.
This is because most if not all card readers are peripherals to the POS and most POS systems have yet to be upgraded to support chip.
In the UK often the card machine is entirely independent of the cash register.
When my employer got new card machines, the model supported contactless, but only CMS given the POS it was attached to. It only worked with Discover Zip. I still had to sign.
Visa Pay-wave would decline. None of my colleagues ever saw contactless before and the signature screen never even showed the logo. Verifone Mx925
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I was caught out by this recently; didn’t realise it was a magstripe issue so ended up paying through HSBC for french transactions. VERY EXPENSIVE 
Shopto still not accepting Monzo. Gets declined every time.
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I had an online purchase at H.Samuel declined. Would accept other forms of payment but not Monzo!
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